Research Interests

Professor Warshauer received his Ph.D. from Louisiana State University in 1979. He has worked on research in number theory, computer science, analysis of algorithms, and mathematics education. He founded Mathworks as a center for mathematics education in 1990, with three pillars being summer mathematics programs, curriculum development, and teacher training. His current research interest is focused on research and development of mathematics education research projects in each of these areas, and building a strong research group that supports related research projects described below.

The Junior Summer Math Camp (JSMC) for middle school students prepares students for algebra and higher level mathematics, while introducing a rich curriculum including problem solving and contest mathematics. A team of students from the JSMC competes each year in the Primary Math World Contest in Hong Kong. The JSMC includes both commuter students and a residential program, with students from throughout Texas as well as other countries attending each year. The Honors Summer Math Camp (HSMC) for high school students is a 6 week residential program with 60 students and 15 counselors. Students learn to think deeply of simple things, following the Ross Model from Ohio State. Courses include Number Theory, an Honors Seminar, Mathematica programming, Combinatorics, Analysis and Abstract Algebra. Advanced students work with mentors on research projects that are submitted to the Siemens Competition. Research projects about these programs include studying the impact of out-of-school programs on selected populations, and using the camps as a laboratory to develop new ideas in teaching and learning mathematics. Future research projects include using the international connections of Mathworks to study and compare best practices with programs in other countries.

In curriculum development, Dr. Warshauer has worked with his colleagues to develop a middle school curriculum, Math Explorations (ME), that is now state adopted in Texas. ME is unique in that it weaves in algebraic concepts and algebra throughout. An associated teacher training program introduces pre-service and in-service curriculum to the curriculum and how to teach it effectively. Research projects include studying the fidelity of the curriculum implementation, developing the critical elements of success for schools that use ME, studying teacher mathematical knowledge for teaching, and developing videos to enhance teacher training. Projects related to using technology to support learning mathematics that could be used along with the curriculum is an exciting new area for further research and development.

Teaching Philosophy

The reason that I teach is because of the joy that comes from seeing my students realize that they each have the ability to contribute to society in so many ways.

I especially enjoy teaching Number Theory each year to students ranging from high school students in summer math camps to undergraduate music majors to graduate students in mathematics. Number theory is ideally suited for students with different math backgrounds since the concepts are developed based on simple examples. The key is to not take things for granted, to be clear about what we assume, and to encourage the students to become active participants in every class. In this setting, I have found that all students are capable of amazing accomplishments; the challenge is to inspire students to realize how much they can do for themselves.

My problem sets reflect this basic philosophy including problems to "Prove or Disprove and Salvage if Possible". Numerical problems and examples lead to patterns that encourage students to make conjectures and question why things work. The students see that not all of our conjectures are true and they develop the ability to make new discoveries for themselves. Math class is not just a time for me to lecture the students, but a time when students can discuss their proofs and learn from one another by working together. In mathematics, there arre often multiple ways to do a problem and discussing mathematics with others enables students to understand the subtle, simple ideas that can lead to new discoveries. The best way to learn an ideas is to explain what you are doing to someone else. The process of having students explain their proofs in class helps all students learn more.

Teaching mathematics involves much more than numbers and facts; it involves building character, instilling confidence, and nurturing a student's creativity and imagination. Students develop a foundation that will enable them to analyze problems critically in any area with a passion for learning and a deep understanding of how working together they can solve problems that alone may have seemed insurmountable.

Recent Talks and Presentations

Invited Keynote Speaker, “Mathworks, Math Problems, and Math Education Research,” International Conference on Recent Research and Issues in Mathematics, Sciences, Technology, Education, and their Applications, State University of Makassar, August 20, 2014.

“Research Problems and Opportunities in Mathematics Education,” General invited Lecture on Mathematics: Education, Development and Research to undergraduates and teachers, State University of Makassar, Aug. 21, 2014.